An increasing number of recent applications rely on the solution of nonlinear semide nite programs. First and second order optimality conditions for nonlinear programs are widely known today. This paper presents a self-contained generalization of these optimality conditions to nonlinear semide nite programs, highlighting some parallels and some di erences. It starts by discussing a constraint q...

In this paper, several new applications for subspace methods are introduced, including: (1) a subspace method used for overcoming generalization/overrtting problem for applications such as face recognition, (2) multiple subspaces constructed from the original sub-space to accommodate the inputs distorted by scaling, rotating, translating etc, and (3) a subspace framework based on which the orig...

Factor analysis and principal components analysis can be used to model linear relationships between observed variables and linearly map high-dimensional data to a lower-dimensional hidden space. In factor analysis, the observations are modeled as a linear combination of normally distributed hidden variables. We describe a nonlinear generalization of factor analysis , called "product analysis", ...

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identificat...

Wheeled mobile robot control method based on SVM algorithm and nonlinear control laws is discussed in this paper. The control system includes two parts: nonlinear controller and SVM controller. Nonlinear controller’s primary role is to obtain the desired velocity which can make the kinematics stable, SVM controller’s primary role is to optimize the control parameters through on-line learning an...

We report on the first realization of a single bosonic Josephson junction, implemented by two weakly linked Bose-Einstein condensates in a double-well potential. In order to fully investigate the nonlinear tunneling dynamics we measure the density distribution in situ and deduce the evolution of the relative phase between the two condensates from interference fringes. Our results verify the pre...

Two new integrable nonlocal Davey–Stewartson equations are introduced. These equations provide two-spatial dimensional analogues of the integrable, nonlocal nonlinear Schrö-dinger equation introduced in Ablowitz and Musslimani (2013 Phys. Rev. Lett. 110 064105). Furthermore, like the latter equation, they also possess a PT symmetry and, as it is well known, this symmetry is important for the ...

We consider a class of nonlinear estimation problems possessing certain algebraic properties, and we exploit these properties in order to study the computational complexity of nonlinear estimation algorithms. Specifically, we define a class of finite-state Markov processes evolving on finite groups and consider noisy observations of these processes. By introducing some concepts from the theory ...